7,418 research outputs found
Towards Practical Typechecking for Macro Tree Transducers
Macro tree transducers (mtt) are an important model that both covers many
useful XML transformations and allows decidable exact typechecking. This paper
reports our first step toward an implementation of mtt typechecker that has a
practical efficiency. Our approach is to represent an input type obtained from
a backward inference as an alternating tree automaton, in a style similar to
Tozawa's XSLT0 typechecking. In this approach, typechecking reduces to checking
emptiness of an alternating tree automaton. We propose several optimizations
(Cartesian factorization, state partitioning) on the backward inference process
in order to produce much smaller alternating tree automata than the naive
algorithm, and we present our efficient algorithm for checking emptiness of
alternating tree automata, where we exploit the explicit representation of
alternation for local optimizations. Our preliminary experiments confirm that
our algorithm has a practical performance that can typecheck simple
transformations with respect to the full XHTML in a reasonable time
Pebble alternating tree-walking automata and their recognizing power
Pebble tree-walking automata with alternation were first investigated by Milo, Suciu and Vianu (2003), who showed that tree languages recognized by these devices are exactly the regular tree languages. We strengthen this by proving the same result for pebble automata with "strong pebble handling" which means that pebbles can be lifted independently of the position of the reading head and without moving the reading head. Then we make a comparison among some restricted versions of these automata. We will show that the deterministic and non-looping pebble alternating tree-walking automata are strictly less powerful than their nondeterministic counterparts, i.e., they do not recognize all the regular tree languages. Moreover, there is a proper hierarchy of recognizing capacity of deterministic and non-looping n-pebble alternating tree-walking automata with respect to the number of pebbles, i.e., for each n ≥ 0, deterministic and non-looping (n+1)-pebble alternating tree-walking automata are more powerful than their n-pebble counterparts
Alternating register automata on finite words and trees
We study alternating register automata on data words and data trees in
relation to logics. A data word (resp. data tree) is a word (resp. tree) whose
every position carries a label from a finite alphabet and a data value from an
infinite domain. We investigate one-way automata with alternating control over
data words or trees, with one register for storing data and comparing them for
equality. This is a continuation of the study started by Demri, Lazic and
Jurdzinski. From the standpoint of register automata models, this work aims at
two objectives: (1) simplifying the existent decidability proofs for the
emptiness problem for alternating register automata; and (2) exhibiting
decidable extensions for these models. From the logical perspective, we show
that (a) in the case of data words, satisfiability of LTL with one register and
quantification over data values is decidable; and (b) the satisfiability
problem for the so-called forward fragment of XPath on XML documents is
decidable, even in the presence of DTDs and even of key constraints. The
decidability is obtained through a reduction to the automata model introduced.
This fragment contains the child, descendant, next-sibling and
following-sibling axes, as well as data equality and inequality tests
Alternating Tree Automata with Qualitative Semantics
We study alternating automata with qualitative semantics over infinite binary trees: Alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the automaton is accepting if almost all branches of the run are accepting. In this article, we prove a positive and a negative result for the emptiness problem of alternating automata with qualitative semantics. The positive result is the decidability of the emptiness problem for the case of BĂĽchi acceptance condition. An interesting aspect of our approach is that we do not extend the classical solution for solving the emptiness problem of alternating automata, which first constructs an equivalent non-deterministic automaton. Instead, we directly construct an emptiness game making use of imperfect information. The negative result is the undecidability of the emptiness problem for the case of co-BĂĽchi acceptance condition. This result has two direct consequences: The undecidability of monadic second-order logic extended with the qualitative path-measure quantifier and the undecidability of the emptiness problem for alternating tree automata with non-zero semantics, a recently introduced probabilistic model of alternating tree automata
Generating Concurrency Checks Automatically
This article introduces ATAB, a tool that automatically generates pairwise
reachability checks for action trees. Action trees can be used to study the
behaviour of real-world concurrent programs. ATAB encodes pairwise reachability
checks into alternating tree automata that determine whether an action tree has
a schedule where any pair of given points in the program are simultaneously
reachable. Because the pairwise reachability problem is undecidable in general
ATAB operates under a restricted form of lock-based concurrency. ATAB produces
alternating tree automata that are more compact and more efficiently checkable
than those that have been previously used. The process is entirely automated,
which simplifies the process of encoding checks for more complex action trees.
The alternating tree automata produced are easier to scale to large numbers of
locks than previous constructions.Comment: 15 pages, 9 figure
On the Borel Inseparability of Game Tree Languages
The game tree languages can be viewed as an automata-theoretic counterpart of
parity games on graphs. They witness the strictness of the index hierarchy of
alternating tree automata, as well as the fixed-point hierarchy over binary
trees. We consider a game tree language of the first non-trivial level, where
Eve can force that 0 repeats from some moment on, and its dual, where Adam can
force that 1 repeats from some moment on. Both these sets (which amount to one
up to an obvious renaming) are complete in the class of co-analytic sets. We
show that they cannot be separated by any Borel set, hence {\em a fortiori} by
any weakly definable set of trees. This settles a case left open by
L.Santocanale and A.Arnold, who have thoroughly investigated the separation
property within the -calculus and the automata index hierarchies. They
showed that separability fails in general for non-deterministic automata of
type , starting from level , while our result settles
the missing case
Relational semantics of linear logic and higher-order model-checking
In this article, we develop a new and somewhat unexpected connection between
higher-order model-checking and linear logic. Our starting point is the
observation that once embedded in the relational semantics of linear logic, the
Church encoding of any higher-order recursion scheme (HORS) comes together with
a dual Church encoding of an alternating tree automata (ATA) of the same
signature. Moreover, the interaction between the relational interpretations of
the HORS and of the ATA identifies the set of accepting states of the tree
automaton against the infinite tree generated by the recursion scheme. We show
how to extend this result to alternating parity automata (APT) by introducing a
parametric version of the exponential modality of linear logic, capturing the
formal properties of colors (or priorities) in higher-order model-checking. We
show in particular how to reunderstand in this way the type-theoretic approach
to higher-order model-checking developed by Kobayashi and Ong. We briefly
explain in the end of the paper how his analysis driven by linear logic results
in a new and purely semantic proof of decidability of the formulas of the
monadic second-order logic for higher-order recursion schemes.Comment: 24 pages. Submitte
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